{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test julia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using BioAlignments\n",
    "using GenomicFeatures\n",
    "using Flux\n",
    "using XAM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "XAM.BAM.Reader{IOStream}:\n",
       "  number of contigs: 194"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bam = \"/mnt/raid64/Covid19_Gravida/cellranger/CG/outs/possorted_genome_bam.bam\"\n",
    "\n",
    "reader = open(BAM.Reader, bam, index=string(bam, \".bai\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# KI270746.1   LN:66486\n",
    "# 2 242193529\n",
    "# KI270394.1 970\n",
    "\n",
    "for record in eachoverlap(reader, \"KI270394.1\", 1:970)\n",
    "    # `record` is a BAM.Record object\n",
    "    # ...\n",
    "    println(record)\n",
    "    break\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Flux"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Flux的居然可以根据情况自动生成梯度递减函数，这个可太爽快了"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "f(x) = 3x^2 + 2x + 1;\n",
    "\n",
    "df(x) = gradient(f, x)[1]; # df/dx = 6x + 2\n",
    "\n",
    "d2f(x) = gradient(df, x)[1]; # d²f/dx² = 6\n",
    "\n",
    "println(df(2))\n",
    "println(d2f(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling Plots [91a5bcdd-55d7-5caf-9e0b-520d859cae80]\n",
      "└ @ Base loading.jl:1278\n"
     ]
    },
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      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "\n",
    "x = [i for i = 1:20]\n",
    "p = plot(x, [f(i) for i = x], label = [\"f\"])\n",
    "p = plot!(p, x, [df(i) for i = x], label = [\"df\"])\n",
    "plot!(p, x, [d2f(i) for i = x], label = [\"d2f\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "简单地线性回归\n",
    "定义了预测函数和loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2352547565793373"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = rand(2, 5)\n",
    "b = rand(2)\n",
    "\n",
    "predict(x) = W*x .+ b\n",
    "\n",
    "function loss(x, y)\n",
    "  ŷ = predict(x)\n",
    "  sum((y .- ŷ).^2)\n",
    "end\n",
    "\n",
    "x, y = rand(5), rand(2) # Dummy data\n",
    "\n",
    "p = plot(x, y, label=\"real\")\n",
    "p = plot!(x, [predict(i) for i = x], label=\"before\")\n",
    "loss(x, y) # ~ 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "根据loss函数可以计算一个合适的梯度下降函数出来，并且根据梯度下降的结果，更新权重矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.282920997646739"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs = gradient(() -> loss(x, y), params(W, b))\n",
    "\n",
    "W̄ = gs[W]\n",
    "\n",
    "W .-= 0.1 .* W̄\n",
    "\n",
    "loss(x, y) # ~ 2.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. 构建图层（毕竟深度学习框架）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 2.358470977542008\n",
       " 2.554117136535825"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W1 = rand(3, 5)\n",
    "b1 = rand(3)\n",
    "layer1(x) = W1 * x .+ b1\n",
    "\n",
    "W2 = rand(2, 3)\n",
    "b2 = rand(2)\n",
    "layer2(x) = W2 * x .+ b2\n",
    "\n",
    "model(x) = layer2(σ.(layer1(x)))\n",
    "\n",
    "model(rand(5)) # => 2-element vectorgs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "两种比较优雅的方式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       "  0.7341020493389869\n",
       " -4.153105295628998"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function linear(in, out)\n",
    "  W = randn(out, in)\n",
    "  b = randn(out)\n",
    "  x -> W * x .+ b\n",
    "end\n",
    "\n",
    "linear1 = linear(5, 3) # we can access linear1.W etc\n",
    "linear2 = linear(3, 2)\n",
    "\n",
    "model(x) = linear2(σ.(linear1(x)))\n",
    "\n",
    "model(rand(5)) # => 2-element vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Float64,1}:\n",
       "  5.17544078110745\n",
       " -1.9842478030097381\n",
       "  2.3855876852960747\n",
       "  0.6622898637967336\n",
       "  2.3689760505523467"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "struct Affine\n",
    "  W\n",
    "  b\n",
    "end\n",
    "\n",
    "Affine(in::Integer, out::Integer) =\n",
    "  Affine(randn(out, in), randn(out))\n",
    "\n",
    "# Overload call, so the object can be used as a function\n",
    "(m::Affine)(x) = m.W * x .+ m.b\n",
    "\n",
    "a = Affine(10, 5)\n",
    "\n",
    "a(rand(10)) # => 5-element vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Flux提供了诸多函数，辅助构建layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float32,1}:\n",
       " 0.59607226\n",
       " 0.40392777"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2 = Chain(\n",
    "  Dense(10, 5, σ),\n",
    "  Dense(5, 2),\n",
    "  softmax)\n",
    "\n",
    "model2(rand(10)) # => 2-element vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float32,1}:\n",
       " 0.49848306\n",
       " 0.4304043"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = Dense(5, 2) ∘ Dense(10, 5, σ)\n",
    "\n",
    "m(rand(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = Chain(x -> x^2, x -> x+1)\n",
    "\n",
    "m(5) # => 26"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 简单构建一个线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling Distributions [31c24e10-a181-5473-b8eb-7969acd0382f]\n",
      "└ @ Base loading.jl:1278\n"
     ]
    }
   ],
   "source": [
    "using Distributions\n",
    "using Flux\n",
    "using Random\n",
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(100)\n",
    "x = rand(Normal(), 100)\n",
    "\n",
    "Random.seed!(100)\n",
    "y = 3 .* x .^ 2 .+ 2 .+ 0.2 * rand(Normal(), 100)\n",
    "\n",
    "plot(x, y, seriestype = :scatter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×1 Array{Float64,2}:\n",
       " 0.2601250914736861"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(100)\n",
    "w1 = rand(Float64, (1, 1))\n",
    "\n",
    "Random.seed!(100)\n",
    "b1 = rand(Float64, (1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 0.001\n",
    "max_iters = 800\n",
    "y_pred = Vector()\n",
    "for i = 1:max_iters\n",
    "    y_pred = x .^ 2 .* w1 .+ b1\n",
    "    \n",
    "    loss = sum(0.5 .* (y_pred - y) .^ 2)\n",
    "    \n",
    "    grad_w = sum((y_pred .- y) .* x .^ 2)\n",
    "    grad_b = sum(y_pred .- y)\n",
    "    \n",
    "    w1 = w1 .- (grad_w * lr)\n",
    "    b1 = b1 .- (grad_b * lr)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(x, y, seriestype = :scatter)\n",
    "plot!(p, x, y_pred, seriestype = :scatter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flux实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "loss (generic function with 1 method)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 定义线性相关的函数\n",
    "f(x) = x .^ 2 .* w1 .+ b1;\n",
    "\n",
    "# 随机生成w和b\n",
    "Random.seed!(100)\n",
    "w1 = rand(Float64, (1, 1))\n",
    "\n",
    "Random.seed!(100)\n",
    "b1 = rand(Float64, (1, 1))\n",
    "\n",
    "Random.seed!(100)\n",
    "x = rand(Normal(), 100)\n",
    "\n",
    "Random.seed!(100)\n",
    "y = 3 .* x .^ 2 .+ 2 .+ 0.2 * rand(Normal(), 100)\n",
    "\n",
    "# 自定义loss函数\n",
    "function loss(x, y)\n",
    "  ŷ = f(x)\n",
    "  sum(0.5 * (y .- ŷ).^2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x, y, label=\"real\", seriestype = :scatter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_iters = 5000\n",
    "for i = 1:max_iters\n",
    "    gs = gradient(() -> loss(x, y), Flux.params(w1, b1))\n",
    "    w1 .-= lr .* gs[w1]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(x, y, seriestype = :scatter)\n",
    "plot!(p, x, collect(Iterators.flatten(f.(x))), seriestype = :scatter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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